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Unformatted text preview: of slightly diﬀerent absolute values,
we make the fern look less symmetric and so more natural. Ofcourse, these two
rules alone will not prodce the bottom two fronds. These must be used together
with the other rules for the fern.
r
s
0.30
0.34
0.30
0.37
Rules for the θ
49◦
50◦
bottom ϕ
49◦
50◦
left and e
f
0
1.60
0
0.44
right fronds. 70 CHAPTER 2. ITERATED FUNCTION SYSTEMS Now imagine snipping oﬀ the bottom left and right fronds and all the stem up
to the bottom left frond. What remains is a copy of the fern, not much smaller
than the original, rotated a little to give the fern its overall curl, and translated
vertically.
r
s
θ
ϕ
e
f
0.85
0.85
2.5◦
2.5◦
0
1.60
Rule for everything above the bottom two fronds.
Combining these three rules gives the picture on the left of Fig. 2.36. Obviously, Figure 2.36: Left: fractal fern without stem. Right: fractal fern with its main
pieces pulled apart.
we’ve missed the bottom of the stem of the fern. But notice a consequence of
fractality: if...
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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.
 Fall '14
 AmandaFolsom
 Geometry, Fractal Geometry, Limits, The Land

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